The German joins the Swiss team after a year racing for Force India, having previously had a spell at Williams.
Chief designer Matt Morris told Autosport: "I worked with Nico briefly at Williams and he's not only a fast driver, he's also a clever driver.
"That's both in terms of his general approach and also his ability to understanding engineering. He's a huge asset to the team."
The 25-year-old finished 11th in the drivers' championship last season.